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If $f(x)=[x]^{2}-5[x]+6=0$, where $[x]$ denotes greatest integer function
then $x \in$
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then $x \in$
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Verified Answer
The correct answer is:
$[2,4)$
We have, $[x]^{2}-5[x]+6=0$
$\therefore([x]-3)([x]-2)=0 \Rightarrow[x]=2,3$
For $[x]=2, x \in[2,3)$ and for $[x]=3, x \in[3,4)$
$\therefore \quad x \in[2,4)$
$\therefore([x]-3)([x]-2)=0 \Rightarrow[x]=2,3$
For $[x]=2, x \in[2,3)$ and for $[x]=3, x \in[3,4)$
$\therefore \quad x \in[2,4)$
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